Chapter 6 Dimensionality Reduction with Principal Component Analysis (PCA)

High-dimensional data, such as images, often pose challenges for analysis, visualization, and storage. For instance, a 640×480 color image represents a point in a million-dimensional space (three dimensions per pixel). Despite this complexity, high-dimensional data usually contains redundancy and correlation, allowing it to be represented in a lower-dimensional space with minimal loss of information.

Dimensionality reduction leverages these redundancies to produce a more compact representation of the data—similar to compression techniques like JPEG (for images) or MP3 (for audio).